the mathematics of medical imaging springer undergraduate texts in mathematics and technology

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The Mathematics Of Medical Imaging

Author : Timothy G. Feeman
ISBN : 9783319226651
Genre : Mathematics
File Size : 49. 93 MB
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The basic mathematics of computerized tomography, the CT scan, are aptly presented for an audience of undergraduates in mathematics and engineering. Assuming no prior background in advanced mathematical analysis, topics such as the Fourier transform, sampling, and discrete approximation algorithms are introduced from scratch and are developed within the context of medical imaging. A chapter on magnetic resonance imaging focuses on manipulation of the Bloch equation, the system of differential equations that is the foundation of this important technology. Extending the ideas of the acclaimed first edition, new material has been adeed to render an even more accessible textbook for course usage. This edition includes new discussions of the Radon transform, the Dirac delta function and its role in X-ray imaging, Kacmarz’s method and least squares approximation, spectral filtering, and more. Copious examples and exercises, new computer-based exercises, and additional graphics have been added to further delineate concepts. The use of technology has been revamped throughout with the incorporation of the open source programming environment R to illustrate examples and composition of graphics. All R code is available as extra source material on SpringerLink. From the reviews of the first edition: “This book is valuable, for it addresses with care and rigor the relevance of a variety of mathematical topics to a real-world problem. ...T his book is well written. It serves its purpose of focusing a variety of mathematical topics onto a real-world application that is in its essence mathematics.” –The Journal of Nuclear Medicine, Vol. 51 (12), December, 2010 “This new book by Timothy Feeman, truly intended to be a beginner’s guide, makes the subject accessible to undergraduates with a working knowledge of multivariable calculus and some experience with vectors and matrix methods. handles the material with clarity and grace...” –The Mathematical Association of America, February, 2010

Mathematik Und Technologie

Author : Christiane Rousseau
ISBN : 9783642300929
Genre : Mathematics
File Size : 26. 79 MB
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Zusammen mit der Abstraktion ist die Mathematik das entscheidende Werkzeug für technologische Innovationen. Das Buch bietet eine Einführung in zahlreiche Anwendungen der Mathematik auf dem Gebiet der Technologie. Meist werden moderne Anwendungen dargestellt, die heute zum Alltag gehören. Die mathematischen Grundlagen für technologische Anwendungen sind dabei relativ elementar, was die Leistungsstärke der mathematischen Modellbildung und der mathematischen Hilfsmittel beweist. Mit zahlreichen originellen Übungen am Ende eines jeden Kapitels.

Modellbildung Und Simulation

Author : Hans-Joachim Bungartz
ISBN : 9783642376566
Genre : Computers
File Size : 83. 77 MB
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Dieses Buch gibt eine Einführung in die mathematische und informatische Modellierung sowie in die Simulation als universelle Methodik. Und so geht es um Klassen von Modellen, um deren Herleitung und um die Vielfalt an Beschreibungsarten, die eingesetzt werden können – diskret oder kontinuierlich, deterministisch oder stochastisch. Aber immer geht es auch darum, wie aus unterschiedlichen abstrakten Modellen ganz konkrete Simulationsergebnisse gewonnen werden können. Nach einem kompakten Repetitorium zum benötigten mathematischen Apparat wird das Konzept „Über das Modell zur Simulation" anhand von 14 Szenarien aus den Bereichen „Spielen – entscheiden – planen", „Verkehr auf Highways und Datenhighways", „Dynamische Systeme" sowie „Physik im Rechner" umgesetzt. Ob Spieltheorie oder Finanzmathematik, Verkehr oder Regelung, ob Populationsdynamik oder Chaos, Molekulardynamik, Kontinuumsmechanik oder Computergraphik – der Leser erhält auf anschauliche und doch systematische Weise Einblicke in die Welt der Modelle und Simulationen.

Image Analysis And Recognition

Author : Aurélio Campilho
ISBN : 9783319117553
Genre : Computers
File Size : 30. 44 MB
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The two volumes LNCS 8814 and 8815 constitute the thoroughly refereed proceedings of the 11th International Conference on Image Analysis and Recognition, ICIAR 2014, held in Vilamoura, Portugal, in October 2014. The 107 revised full papers presented were carefully reviewed and selected from 177 submissions. The papers are organized in the following topical sections: image representation and models; sparse representation; image restoration and enhancement; feature detection and image segmentation; classification and learning methods; document image analysis; image and video retrieval; remote sensing; applications; action, gestures and audio-visual recognition; biometrics; medical image processing and analysis; medical image segmentation; computer-aided diagnosis; retinal image analysis; 3D imaging; motion analysis and tracking; and robot vision.

Emergency Radiology Of The Chest And Cardiovascular System

Author : Mariano Scaglione
ISBN : 9783319425849
Genre : Medical
File Size : 84. 86 MB
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This book provides an up-to-date, systematic review of all facets of emergency radiology in patients with chest trauma or pain with the aim of equipping the reader with a detailed knowledge of the various radiological patterns, which is essential in order to make a prompt diagnosis under circumstances when time is of critical importance. To this end, the indications, value, and results of the various emergency imaging modalities, including sonography and interventional radiology, are described and illustrated in the full range of blunt chest injuries and nontraumatic chest emergencies. Technological aspects, protocols tailored to the mechanism of injury, and post-processing techniques are also extensively covered. Emergency Radiology of the Chest and Cardiovascular System will be of value to general and interventional radiologists, radiology residents, radiology technicians, and all physicians and surgeons who work in emergency care.

Applied Fourier Analysis

Author : Tim Olson
ISBN : 9781493973934
Genre : Mathematics
File Size : 44. 50 MB
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The first of its kind, this focused textbook serves as a self-contained resource for teaching from scratch the fundamental mathematics of Fourier analysis and illustrating some of its most current, interesting applications, including medical imaging and radar processing. Developed by the author from extensive classroom teaching experience, it provides a breadth of theory that allows students to appreciate the utility of the subject, but at as accessible a depth as possible. With myriad applications included, this book can be adapted to a one or two semester course in Fourier Analysis or serve as the basis for independent study. Applied Fourier Analysis assumes no prior knowledge of analysis from its readers, and begins by making the transition from linear algebra to functional analysis. It goes on to cover basic Fourier series and Fourier transforms before delving into applications in sampling and interpolation theory, digital communications, radar processing, medi cal imaging, and heat and wave equations. For all applications, ample practice exercises are given throughout, with collections of more in-depth problems built up into exploratory chapter projects. Illuminating videos are available on and that present animated visualizations of several concepts. The content of the book itself is limited to what students will need to deal with in these fields, and avoids spending undue time studying proofs or building toward more abstract concepts. The book is perhaps best suited for courses aimed at upper division undergraduates and early graduates in mathematics, electrical engineering, mechanical engineering, computer science, physics, and other natural sciences, but in general it is a highly valuable resource for introducing a broad range of students to Fourier analysis.

Wissenschaftliches Rechnen Mit Matlab

Author : Alfio Quarteroni
ISBN : 9783540293071
Genre : Mathematics
File Size : 80. 72 MB
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Aus den Rezensionen der englischen Auflage: Dieses Lehrbuch ist eine Einführung in das Wissenschaftliche Rechnen und diskutiert Algorithmen und deren mathematischen Hintergrund. Angesprochen werden im Detail nichtlineare Gleichungen, Approximationsverfahren, numerische Integration und Differentiation, numerische Lineare Algebra, gewöhnliche Differentialgleichungen und Randwertprobleme. Zu den einzelnen Themen werden viele Beispiele und Übungsaufgaben sowie deren Lösung präsentiert, die durchweg in MATLAB formuliert sind. Der Leser findet daher nicht nur die graue Theorie sondern auch deren Umsetzung in numerischen, in MATLAB formulierten Code. MATLAB select 2003, Issue 2, p. 50. [Die Autoren] haben ein ausgezeichnetes Werk vorgelegt, das MATLAB vorstellt und eine sehr nützliche Sammlung von MATLAB Funktionen für die Lösung fortgeschrittener mathematischer und naturwissenschaftlicher Probleme bietet. [...] Die Präsentation des Stoffs ist durchgängig gut und leicht verständlich und beinhaltet Lösungen für die Übungen am Ende jedes Kapitels. Als exzellenter Neuzugang für Universitätsbibliotheken- und Buchhandlungen wird dieses Buch sowohl beim Selbststudium als auch als Ergänzung zu anderen MATLAB-basierten Büchern von großem Nutzen sein. Alles in allem: Sehr empfehlenswert. Für Studenten im Erstsemester wie für Experten gleichermassen. S.T. Karris, University of California, Berkeley, Choice 2003.

An Introduction To Complex Systems

Author : Paul Fieguth
ISBN : 9783319446066
Genre : Science
File Size : 20. 13 MB
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This undergraduate text explores a variety of large-scale phenomena - global warming, ice ages, water, poverty - and uses these case studies as a motivation to explore nonlinear dynamics, power-law statistics, and complex systems. Although the detailed mathematical descriptions of these topics can be challenging, the consequences of a system being nonlinear, power-law, or complex are in fact quite accessible. This book blends a tutorial approach to the mathematical aspects of complex systems together with a complementary narrative on the global/ecological/societal implications of such systems. Nearly all engineering undergraduate courses focus on mathematics and systems which are small scale, linear, and Gaussian. Unfortunately there is not a single large-scale ecological or social phenomenon that is scalar, linear, and Gaussian. This book offers students insights to better understand the large-scale problems facing the world and to realize that these cannot be solved by a single, narrow academic field or perspective. Instead, the book seeks to emphasize understanding, concepts, and ideas, in a way that is mathematically rigorous, so that the concepts do not feel vague, but not so technical that the mathematics get in the way. The book is intended for undergraduate students in a technical domain such as engineering, computer science, physics, mathematics, and environmental studies.

Bone Quantitative Ultrasound

Author : Pascal Laugier
ISBN : 9400700172
Genre : Medical
File Size : 23. 9 MB
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Quantitative ultrasound (QUS) of bone is a relatively recent research field. The research community is steadily growing, with interdisciplinary branches in acoustics, medical imaging, biomechanics, biomedical engineering, applied mathematics, bone biology and clinical sciences, resulting in significant achievements in new ultrasound technologies to measure bone, as well as models to elucidate the interaction and the propagation of ultrasonic wave in complex bone structures. Hundreds of articles published in specialists journals are accessible from the Web and from electronic libraries. However, no compilation and synthesis of the most recent and significant research exist. The only book on QUS of bone has been published in 1999 at a time when the propagation mechanisms of ultrasound in bone were still largely unknown and the technology was immature. The research community has now reached a critical size, special sessions are organized in major international meetings (e.g., at the World Congress of Biomechanics, the annual meetings of the Acoustical Society of America, International Bone Densitometry Workshop, etc...). Consequently, the time has come for a completely up to date, comprehensive review of the topic. The book will offer the most recent experimental results and theoretical concepts developed so far and is intended for researchers, graduate or undergraduate students, engineers, and clinicians who are involved in the field. The central part of the book covers the physics of ultrasound propagation in bone. Our goal is to give the reader an extensive view of the mathematical and numerical models as an aid to understand the QUS potential and the types of variables that can be determined by QUS in order to characterize bone strength. The propagation of sound in bone is still subject of intensive research. Different models have been proposed (for example, the Biot theory of poroelasticity and the theory of scattering have been used to describe wave propagation in cancellous bone, whereas propagation in cortical bone falls in the scope of guided waves theories). An extensive review of the models has not been published so far. We intend in this book to present in details the models that are used to solve the direct problem and strategies that are currently developed to address the inverse problem. This will include analytical theories and numerical approaches that have grown exponentially in recent years. Most recent experimental findings and technological developments will also be comprehensively reviewed.

Computational Hemodynamics Theory Modelling And Applications

Author : Jiyuan Tu
ISBN : 9789401795944
Genre : Technology & Engineering
File Size : 65. 76 MB
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This book discusses geometric and mathematical models that can be used to study fluid and structural mechanics in the cardiovascular system. Where traditional research methodologies in the human cardiovascular system are challenging due to its invasive nature, several recent advances in medical imaging and computational fluid and solid mechanics modelling now provide new and exciting research opportunities. This emerging field of study is multi-disciplinary, involving numerical methods, computational science, fluid and structural mechanics, and biomedical engineering. Certainly any new student or researcher in this field may feel overwhelmed by the wide range of disciplines that need to be understood. This unique book is one of the first to bring together knowledge from multiple disciplines, providing a starting point to each of the individual disciplines involved, attempting to ease the steep learning curve. This book presents elementary knowledge on the physiology of the cardiovascular system; basic knowledge and techniques on reconstructing geometric models from medical imaging; mathematics that describe fluid and structural mechanics, and corresponding numerical/computational methods to solve its equations and problems. Many practical examples and case studies are presented to reinforce best practice guidelines for setting high quality computational models and simulations. These examples contain a large number of images for visualization, to explain cardiovascular physiological functions and disease. The reader is then exposed to some of the latest research activities through a summary of breakthrough research models, findings, and techniques. The book’s approach is aimed at students and researchers entering this field from engineering, applied mathematics, biotechnology or medicine, wishing to engage in this emerging and exciting field of computational hemodynamics modelling.

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